Constant force acting on a particle

[Vibhor]

Homework Statement

Homework Equations

The Attempt at a Solution

If I consider a coordinate system with the -Y axis along the direction of force and X axis along a line perpendicular to it (except the direction of velocity vector) then this problem is equivalent to the usual projectile motion problem where a particle is projected from an elevation horizontally ( i.e velocity perpendicular to gravity ) .

So I can conclude that the path in the problem is parabolic i.e option b) which is indeed the given answer .

Now , when I tried to find the equation of trajectory , I am a bit lost .

In the usual X-Y coordinate system with 'm' representing the mass of the particle , we have ,

$x = 3t + \frac{1}{2}\frac{4}{m}t^2$

$y = 4t - \frac{1}{2}\frac{3}{m}t^2$

I am finding it difficult to solve the above equations so as to get the relation between x and y .

Any sincere help is very much appreciated .

Thanks .

 

[blue_leaf77]

Calculate $3x+4y$ to eliminate the quadratic terms in $t$. Then solve this for $t$ and substitute for $t$ in either $x(t)$ or $y(t)$. You should get a parabola tilted at 45 degrees.

 

[Vibhor]

Calculate $3x+4y$ to eliminate the quadratic terms in $t$. Then solve this for $t$ and substitute for $t$ in either $x(t)$ or $y(t)$. You should get a parabola tilted at 45 degrees.

Fantastic !

But on expanding I get a term containing $xy$ . I have never really seen an $xy$ term in the usual parabola equations .

 

[blue_leaf77]

Fantastic !

But on expanding I get a term containing $xy$ . I have never really seen an $xy$ term in the usual parabola equations .

The coupled terms like that in conic sections such as parabola is an indication that this curve is rotated at an angle from $x$ or $y$ axis.

 

[Vibhor]

The coupled terms like that in conic sections such as parabola is an indication that this curve is rotated at an angle from $x$ or $y$ axis.

Interesting .

Thanks a lot .